Question

prove that every cyclic qud. is a rectangle

Answer 1

For any quadrilateral to be cyclic the sum of the opposite angles should be 180 deg. ... Congruent supplementary angles are right angles, so opposite angles in a cyclic parallelogram are right angles. Thus all four angles are right angles, and it's a rectangle.

Answer 2

Hello mate ☺

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Solution:

➡It is given that parallelogram ABCD is cyclic. We need to prove that ABCD is a rectangle.

∠B=∠D   (Opposite angles of a parallelogram are equal) ....(1)

∠B+∠D=180°   ...... (2)  

(Sum of opposite angles of a cyclic quadrilateral is equal to 180°)                    

Using equation (1) in equation (2), we get

∠B+∠B=180°

⇒2∠B=180°

⇒∠B=180/2=90°      …...(3)

➡Therefore, ABCD is a parallelogram with ∠B=90° which means that ABCD is a rectangle.

I hope, this will help you.☺

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